not sure I follow you. By category I assume you mean a custom taxonomy… category is default taxonomy of post and as I clarified above you can map a form to an existing post type.
You can create taxonomies associated to the custom post type you map to a form.
Custom taxonomies are by default associated with select/checkbox/radio buttons. So you can map a taxonomy to either one of these type of fields in your form. Once mapped, any terms in your taxonomy will automatically get populated in your mapped field for a user to select/check.
If by text field you mean to have the ability to created new terms for a taxonomy from the field itself, you can enable this and use the built-in filters provided to ensure the new terms is added to the taxonomy as the time of form submission.